-    LiNbO3     -    LiNbO3

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from an experimental structure similar to the one reported in AMCSD 

Crystal Structure 


Because of the translational symmetry all the calculations are performed in the primitive unit cell and not in the conventional unit cell. The following information regarding the structure is given with respect to this primitive unit cell, which sometimes can take an unintuitive shape.

Symmetry (experimental): 

Space group:  161  R3c 
Lattice parameters (Å):  5.4294  5.4294  5.4294 
Angles (°):  55.63  55.63  55.63 

Symmetry (theoretical): 

Space group:  161  R3c 
Lattice parameters (Å):  5.4281  5.4281  5.4281 
Angles (°):  55.88  55.88  55.88 

Cell contents: 

Number of atoms:  10 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Nb:  0.9932  0.9932  0.9932 
Nb:  0.4932  0.4932  0.4932 
Li:  0.2794  0.2794  0.2794 
Li:  0.7794  0.7794  0.7794 
O:  0.7228  0.3737  0.1065 
O:  0.1065  0.7228  0.3737 
O:  0.3737  0.1065  0.7228 
O:  0.8737  0.2228  0.6065 
O:  0.6065  0.8737  0.2228 
O:  0.2228  0.6065  0.8737 
Atom type 

We have listed here the reduced coordinates of all the atoms in the primitive unit cell.
It is enough to know only the position of the atoms from the assymetrical unit cell and then use the symmetry to build the whole crystal structure.

Visualization of the crystal structure: 

Size:

  
Nx:  Ny:  Nz:    
You can define the size of the supercell to be displayed in the jmol panel as integer translations along the three crys­tallo­gra­phic axis.
Please note that the structure is represented using the pri­mi­tive cell, and not the conventional one.
     

Powder Raman 

Powder Raman spectrum

The intensity of the Raman peaks is computed within the density-functional perturbation theory. The intensity depends on the temperature (for now fixed at 300K), frequency of the input laser (for now fixed at 21834 cm-1, frequency of the phonon mode and the Raman tensor. The Raman tensor represents the derivative of the dielectric tensor during the atomic displacement that corresponds to the phonon vibration. The Raman tensor is related to the polarizability of a specific phonon mode.

Horizontal:
Xmin:
Xmax:
Vertical:
Ymin:
Ymax:
 
Choose the polarization of the lasers.
I ∥ 
I ⊥ 
I Total 

Data about the phonon modes

Frequency of the transverse (TO) and longitudinal (LO) phonon modes in the zone-center. The longitudinal modes are computed along the three cartesian directions. You can visualize the atomic displacement pattern corresponding to each phonon by clicking on the appropriate cell in the table below.

1
ac
0
0
0
0
2
ac
0
0
0
0
3
ac
0
0
0
0
4
E
173
173
173
173
1.209e+40
0.8
1.346e+40
0.9
2.555e+40
1.8
5
E
173
182
182
173
1.209e+40
0.8
1.290e+40
0.9
2.499e+40
1.7
6
A2
193
193
193
193
7
E
197
197
197
197
2.408e+41
16.8
3.217e+41
22.5
5.625e+41
39.3
8
E
197
210
210
197
2.408e+41
16.8
2.948e+41
20.6
5.356e+41
37.4
9
A1
210
223
223
241
8.833e+41
61.7
1.318e+41
9.2
1.015e+42
70.9
10
E
241
241
241
241
3.801e+39
0.3
4.322e+39
0.3
8.123e+39
0.6
11
E
241
267
267
263
3.801e+39
0.3
4.073e+39
0.3
7.875e+39
0.6
12
A1
267
297
297
297
4.639e+41
32.4
2.475e+40
1.7
4.887e+41
34.2
13
A2
297
300
300
375
14
E
375
375
375
375
4.179e+39
0.3
3.456e+39
0.2
7.634e+39
0.5
15
E
375
375
375
382
4.179e+39
0.3
4.887e+39
0.3
9.066e+39
0.6
16
E
406
406
406
406
6.772e+40
4.7
7.998e+40
5.6
1.477e+41
10.3
17
E
406
410
410
406
6.772e+40
4.7
7.353e+40
5.1
1.412e+41
9.9
18
A1
410
421
421
412
4.146e+41
29.0
7.091e+36
0.0
4.146e+41
29.0
19
A2
431
431
431
431
20
E
454
454
454
454
1.118e+41
7.8
1.471e+41
10.3
2.590e+41
18.1
21
E
454
469
469
454
1.118e+41
7.8
1.333e+41
9.3
2.451e+41
17.1
22
E
476
476
476
476
2.990e+40
2.1
2.314e+40
1.6
5.304e+40
3.7
23
E
476
494
494
476
2.990e+40
2.1
4.470e+40
3.1
7.460e+40
5.2
24
A2
494
521
521
494
25
A1
649
649
649
671
1.362e+42
95.2
6.890e+40
4.8
1.431e+42
100.0
26
E
671
671
671
671
6.799e+40
4.8
7.517e+40
5.3
1.432e+41
10.0
27
E
671
690
690
694
6.799e+40
4.8
7.244e+40
5.1
1.404e+41
9.8
28
E
694
694
694
694
7.328e+40
5.1
9.508e+40
6.6
1.684e+41
11.8
29
E
694
927
927
929
7.328e+40
5.1
1.159e+41
8.1
1.891e+41
13.2
30
A2
945
945
945
945
No.  Char.  ω TO  ω LOx  ω LOy  ω LOz  I ∥  I ⊥  I Total 
You can define the size of the supercell for the visualization of the vibration.
Nx: 
Ny: 
Nz: 
Normalized
Raw
Options for intensity.